2 Shiva-Parvati, Chola Bronze Q: How was the statue made?A: Invest castingLiquid-to-solid transformationAn example of phase transformationShiva-Parvati, Chola BronzeBall State University
3 Czochralski crystal pulling technique How does one produce single crystal of Si for electronic applications?Czochralski crystal pulling technique
4 Quenching of steel components a solid->solid phase transformation How does one harden a steel component?Quenching of steel components a solid->solid phase transformation
5 Solid state phasetransformationSolid1Solid 2meltingsolidificationsublimationcondensationgasLiquidevaporation
6 Thermodynamic driving force for a phase transformation? Decrease in Gibbs free energyLiquid-> solidgs - gl = g = -ve
7 gGibbs free energy as a function of temperature, Problem 2.3gLgSggL < gSSolid is stableLiquid is stablegS < gLgSgLTTfreezingTmFig. 9.1
8 How does solidification begins? Usually at the walls of the containerHeterogeneous nucleation.Why?To be discussed later.
9 Spherical ball of solid of radius R in the middle of the liquid at a temperature below Tm Homogeneous nucleationrgL = free energy of liquid per unit volumegS = free energy of solid per unit volumeg = gS - gL
10 Change in free energy of the system due to formation of the solid ball of radius r : p24r++ve: barrier to nucleationrrr*
11 Solid balls of radius r < r Solid balls of radius r < r* cannot grow as it will lead to increase in the free energy of the system !!!gp24r+Solid balls of radii r > r* will growrr* is known as the CRITICAL RADIUS OF HOMOGENEOUS NUCLEATIONr*
13 Driving force for solidification TmgLgSTg (T)Eqn. 9.7T
14 g p 4 r + g p 4 r + f Fig. 9.3 f1* f2* r r2* r1* Eqn. 9.7 T2 <
15 Critical particle Fig. 9.4 Atoms surrounding the critical particle Formation of critical nucleus by statistical fluctuationCritical particleDiffuse jump of a surrounding atom to the critical particle makes it a nucleationFig. 9.4
16 The Nucleation RateNt=total number of clusters of atoms per unit volumeN* = number of clusters of critical size per unit volumeBy Maxwell-Boltzmann statistics
17 Eqn. 9.9s*= no. of liquid phase atoms facing the critical sized particleHd = activation energy for diffusive jump from liquid to the solid phase = atomic vibration frequencyThe rate of successful addition of an atom to a critical sized paticleEqn. 9.10
18 1. Driving force increases 2. Atomic mobility decreases Rate of nucleation, I , (m3 s-1)= No. of nucleation events per m3 per sec= number of critical clusters per unit volume (N*)xrate of successful addition of an atom to the critical cluster (’)TEqn. 9.11TmWith decreasing T1. Driving force increases2. Atomic mobility decreasesI
19 GrowthIncrease in the size of a product particle after it has nucleatedTU
20 Overall Transformation Kinetics I : Nucleation rateTUU : Growth ratedX/dtOverall transformation rate (fraction transformed per second)IX=fraction of product phase
21 Fraction transformed as a function of time XSlow due to final impingementSlow due to very few nucleittstf
22 TTT Diagram for liquid-to-solid transformation Xlog ttstf1TTT Diagram for liquid-to-solid transformationdX/dtTTStable liquidTmC- curvesCrystallization beginsL+Crystallization endscrystalUnder Cooled liquidlog t
27 Specific volumeStable liquidUndercooled liquidFast coolFig. 9.18Slow coolcrystalTgfTgsTTm
28 Glass ceramics T log t T T U TU Very fine crystals TI Fig. 9.16 I time Stable liquidTmUndercooled liquidL+devitrificationglasscrystallog tUITTLiquidgrowthTUVery fine crystalsnucleationTIFig. 9.16glassGlass ceramictime
29 Corningware PyroceramTM heat resistant cookware Corning’s new digital hot plates with PyroceramTM tops.ROBAX® was heated until red-hot. Then cold water was poured on the glass ceramic from above - with NO breakage.
30 Czochralski crystal pulling technique for single crystal Si J. Czochralski, ( )Polish MetallurgistSSPL: Solid State Physics Laboratory, N. Delhi
32 HEAT TREATMENTHeating a material to a high temperature, holding it at that temperature for certain length of time followed by cooling at a specified rate is called heat treatment
33 holdingTheatingATAQTNtimeAnnealing Furnace cooling RC 15Normalizing Air cooling RC 30Quenching Water cooling RC 65Tempering Heating after quench RC 55Austempering Quench to an inter- RC mediate temp and hold
34 Ammount of Fe3C in Pearlite Eutectoid Reaction0.80.026.67coolPearliteAmmount of Fe3C in PearliteRed Tie Line below eutectoid temp
35 austenite-> pearlite Phase diagrams do not have any information about time or rates of transformations.We need TTT diagram foraustenite-> pearlitetransformation
36 TTT diagram for eutectoid steel Stable austenitestartfinishunstable austenite
37 TTT diagram for eutectoid steel Stable austeniteunstable austenitestartfinishAnnealing: coarse pearliteNormalizing: fine pearlite
40 Martensitic transformation Amount of martensite formed does not depend upon time, only on temperature.Atoms move only a fraction of atomic distance during the transformation:1. Diffusionless (no long-range diffusion)2. Shear (one-to-one correspondence between and ’ atoms)BCT3. No composition change
41 Martensitic transformation (contd.) Problem 3.1Contract ~ 20%BCT unit cell of (austenite)Expand ~ 12%BCT unit cell of ’ (martensite)0% C (BCC)1.2 % CFig. 9.12
42 Martensitic transformation (contd.) Hardness of martensite as a function of C content6040Hardness, RCFig. 9.13188.8.131.52Wt % Carbon →Hardness of martensite depends mainly on C content and not on other alloying additions
44 TEMPERINGHeating of quenched steel below the eutectoid temperature, holding for a specified time followed by ar cooling.T<TE?
45 Tempering (contd.)+Fe3CPEARLITEA distribution of fine particles of Fe3C in matrix known as TEMPERED MARTENSITE.Hardness more than fine pearlite, ductility more than martensite.Hardness and ductility controlled by tempering temperature and time.Higher T or t -> higher ductility, lower strength
47 AustemperingBainiteShort needles of Fe3C embedded in plates of ferrite
48 Quench CracksProblems in QuenchingHigh rate of cooling:surface cooler than interiorSurface forms martensite before the interiorAustenitemartensiteVolume expansionWhen interior transforms, the hard outer martensitic shell constrains this expansion leading to residual stresses
49 Solution to Quench cracks Shift the C-curve to the right (higher times)More time at the noseSlower quenching (oil quench) can give martensiteBut how to shift the C-curve to higher times?
50 By alloyingAll alloying elements in steel (Cr, Mn, Mo, Ni, Ti, W, V) etc shift the C-curves to the right.Exception: CoSubstitutional diffusion of alloying elements is slower than the interstitial diffusion of C
51 Alloy steelPlain C steelAlloying shifts the C-curves to the right.Fig. 9.10Separate C-curves for pearlite and bainite
52 HardenabilityAbility or ease of hardening a steel by formation of martensite using as slow quenching as possibleAlloying elements in steels shift the C-curve to the rightAlloy steels have higher hardenability than plain C steels.
53 HardnenabilityHardnessResistance to plastic deformation as measured by indentationAbility or ease of hardening a steelOnly applicable to steelsApplicable to all materialsAlloying additions increase the hardenability of steels but not the hardness.C increases both hardenability and hardness of steels.
54 High Speed steelAlloy steels used for cutting tools operated at high speedsCutting at high speeds lead to excessive heating of cutting toolsThis is equivalent to unintended tempering of the tools leading to loss of hardness and cutting edgeAlloying by W gives fine distribution of hard WC particles which counters this reduction in hardness: such steels are known as high speed steels.
57 Alfred Wilm’s Laboratory 1906-1909 Steels harden by quenchingWhy not harden Al alloys also by quenching?
58 Eureka ! Hardness has Increased !! TWilm’s Plan for hardening Al-4%Cu alloyHold550ºCHeatQuenchCheck hardnesstimeSorry! No increase in hardness.Eureka ! Hardness has Increased !!One of the greatest technological achievements of 20th century
59 Hardness increases as a function of time: AGE HARDENING Property = f (microstructure)Wilm checked the microstructure of his age-hardened alloys.Result: NO CHANGE in the microstructure !!
60 Hardness initially increases: age hardening Peak hardnessHardnessOveragingAs- quenched hardnesstimeHardness initially increases: age hardeningAttains a peak valueDecreases subsequently: Overaging
61 : solid solution of Cu in FCC Al + Tsolvus: solid solution of Cu in FCC Al+: intermetallic compound CuAl24supersaturatedsaturated Precipitation of in FCCFCCTetragonal4 wt%Cu0.5 wt%Cu54 wt%Cu
62 TTT diagram of precipitation of in Stable Tsolvus startunstable finsh+As-quenched AgingA fine distribution of precipitates in matrix causes hardeningCompletion of precipitation corresponds to peak hardness
63 -grainsAs quenched-grains + AgedPeak agedDense distribution of fine overagedSparse distribution of coarse Driving force for coarsening/ interfacial energy
64 Aging temperaturehardness100ºC20ºC180ºCFig. 9.15Aging time0.1110100(days)Peak hardness is less at higher aging temperaturePeak hardness is obtained in shorter time at higher aging temperature
65 T U + I 1 start finsh 180 ºC 100 ºC Aging hardness Stable Tsolvus startunstable finsh+180 ºC100 ºCAs-quenched AgingI1hardness180ºC100ºC20ºC
66 Recovery, Recrystallization and grain growth Following slides are courtseyProf. S.K Gupta (SKG)Or Prof. Anandh Subramaniam (AS)
67 AS Plastic deformation in the temperature range above(0.3 – 0.5) Tm → COLD WORK↑ point defect densityCold work↑ dislocation densityPoint defects and dislocations have strain energy associated with them(1 -10) % of the energy expended in plastic deformation is stored in the form of strain energyAS
70 Recovery, Recrystallization and Grain Growth During recovery1. Point Defects come to Equilibrium2. Dislocations of opposite sign lying on a slip plane annihilate each other(This does not lead to substantial decrease in the dislocation density)SKG
71 AS POLYGONIZATION Bent crystal Polygonization Low angle grain boundariesAS
72 Recrystallization Strained grains Strain-free grains Driving force for the Process =Stored strain energy of dislocationsSKG
73 Recrystallization Temperature: Temperature at which the 50% of the cold-worked material recrystallizes in one hourUsually around 0.4 Tm (m.p in K)SKG
74 Factors that affect the recrystallization temperature: 1. Degree of cold work2. Initial Grain Size3. Temperature of cold working4. Purity or composition of metalSolute Drag EffectPinning Action of Second Phase ParticleSKG